On the optimal value function for certain linear programs with unbounded optimal solution sets - Benson, H. P. (Journal of optimization theory and applications, 1985)
Often, the coefficients of a linear programming problem represent estimates of true values of data or are subject to systematic variations. In such cases, it is useful to perturb the original data and to either compute, estimate, or otherwise describe the values of the function f which gives the optimal value of the linear program for each perturbation. The author shows that, frequently, even if the primal problem or the dual problem has an unbounded optimal solution set, the nature of the values of f at points near a given point can be investigated.